Finite Group Databasebeta

← C47×#24367 #26064065

Subgroups — C47×#24367 #26064065

Order 12032.

1604 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×AGL(1,ℤ/8)×C47C211yesmaximal, characteristic
2C2×C47×#463C211yesmaximal, characteristic, complemented
3C2×C47×#461C211yesmaximal, characteristic, complemented
4C2×C47×#450C211yesmaximal, characteristic, complemented
5C47×#2432C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C47C211yesmaximal, characteristic, complemented
7C47×#2055C211yesmaximal, characteristic, complemented
8C47×#2054C211yesmaximal, characteristic, complemented
9C47×#2013C211yesmaximal, characteristic, complemented
10C47×#2012C211yesmaximal, characteristic, complemented
11C47×#1894C211yesmaximal, characteristic, complemented
12C47×#1879C211yesmaximal, characteristic, complemented
13C47×#1877C211yesmaximal, characteristic, complemented
14C47×#1851C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C23×D4×C47C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C47—24no—
19C2×AGL(1,ℤ/8)×C47—24no—
20C2×AGL(1,ℤ/8)×C47—24no—
21C22×SD16×C47C2211yescharacteristic
22C22×SD16×C47C2211yescharacteristic
23C22×SD16×C47C2211yescharacteristic
24C22×SD16×C47C2211yescharacteristic
25C22×D8×C47C2211yescharacteristic
26C22×D8×C47C2211yescharacteristic
27C22×M16×C47C2211yescharacteristic
28C2×C4⋊Q8×C47C2211yescharacteristic, complemented
29C2×#124×C47C2211yescharacteristic, complemented
30C2×C22⋊Q8×C47C2211yescharacteristic
31C2×C4×D4×C47C2211yescharacteristic
32C2×C4×D4×C47C2211yescharacteristic
33C22×C22⋊C4×C47—21no—
34C47×#463—24no—
35C47×#461—24no—
36C47×#450—24no—
37C2×C4⋊C8×C47C2211yescharacteristic, complemented
38C2×C4⋊C8×C47C2211yescharacteristic, complemented
39C2×#103×C47C2211yescharacteristic, complemented
40C2×#103×C47C2211yescharacteristic, complemented
41C2×#103×C47C2211yescharacteristic, complemented
42C2×#103×C47C2211yescharacteristic, complemented
43C2×#102×C47C2211yescharacteristic
44C2×#102×C47C2211yescharacteristic
45C2×#102×C47C2211yescharacteristic, complemented
46C2×#102×C47C2211yescharacteristic, complemented
47C2×C22⋊C8×C47C2211yescharacteristic
48C47×#394—21no—
49C47×#394—21no—
50C47×#391C2211yescharacteristic, complemented
51C47×#390C2211yescharacteristic
52C47×#390C2211yescharacteristic
53C47×#390C2211yescharacteristic, complemented
54C47×#386—21no—
55C47×#386—21no—
56C47×#385—21no—
57C47×#385—21no—
58C47×#380C2211yescharacteristic
59C47×#379—21no—
60C4×C22⋊C4×C47C2211yescharacteristic
61C47×#340C2211yescharacteristic, complemented
62C47×#340C2211yescharacteristic, complemented
63C47×#336C2211yescharacteristic, complemented
64C47×#336C2211yescharacteristic, complemented
65C25×C47—21no—
66C2×#41×C47—22no—
67C2×#41×C47—22no—
68C2×#41×C47—22no—
69C2×#41×C47—22no—
70C2×#41×C47—41no—
71C2×#41×C47—41no—
72C22×Q8×C47C2311yescharacteristic
73C22×Q8×C47C2311yescharacteristic
74C22×D4×C47—22no—
75C22×D4×C47—22no—
76C22×D4×C47—21no—
77C22×D4×C47—21no—
78C22×D4×C47—22no—
79C22×D4×C47—41no—
80C22×D4×C47—41no—
81C22×D4×C47D414yes—
82C22×D4×C47C2311yescharacteristic
83C22×D4×C47C2311yescharacteristic
84C22×D4×C47C2311yescharacteristic
85C23×C4×C47—21no—
86C23×C4×C47—21no—
87C23×C4×C47—21no—
88C23×C4×C47C2311yescharacteristic
89AGL(1,ℤ/8)×C47—232no—
90C2×SD16×C47—22no—
91C2×SD16×C47—22no—
92C2×SD16×C47—22no—
93C2×SD16×C47—22no—
94C2×SD16×C47—22no—
95C2×SD16×C47—22no—
96C2×SD16×C47—22no—
97C2×SD16×C47—22no—
98C2×SD16×C47—22no—
99C2×SD16×C47—41no—
100C2×SD16×C47—41no—
101C2×SD16×C47D414yes—
102C2×D8×C47—22no—
103C2×D8×C47—22no—
104C2×D8×C47—22no—
105C2×D8×C47—22no—
106C2×D8×C47—22no—
107C2×D8×C47D414yes—
108C2×M16×C47—22no—
109C2×M16×C47—22no—
110C2×M16×C47—22no—
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C4⋊Q8×C47—22no—
116C4⋊Q8×C47—41no—
117#124×C47—22no—
118#124×C47—41no—
119C22⋊Q8×C47—22no—
120C22⋊Q8×C47—22no—
121C4×D4×C47—22no—
122C4×D4×C47—22no—
123C4×D4×C47—41no—
124C4×D4×C47—41no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47—21no—
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C4⋊C4×C47C2311yescharacteristic
130C2×C4⋊C4×C47C2311yescharacteristic
131C2×C22⋊C4×C47—21no—
132C2×C22⋊C4×C47—21no—
133C2×C22⋊C4×C47—21no—
134C2×C22⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C22⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C22⋊C4×C47—21no—
139C2×C22⋊C4×C47—21no—
140C2×C22⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C22⋊C4×C47—21no—
143C2×C22⋊C4×C47—44no—
144C2×C22⋊C4×C47D411yescharacteristic
145C2×C22⋊C4×C47D411yescharacteristic
146C2×C42×C47C2311yescharacteristic
147C2×C42×C47C2311yescharacteristic
148C4⋊C8×C47—22no—
149C4⋊C8×C47—22no—
150#103×C47—22no—
151#103×C47—22no—
152#103×C47—22no—
153#103×C47—41no—
154#102×C47—22no—
155#102×C47—22no—
156#102×C47—22no—
157#102×C47—41no—
158C22⋊C8×C47—22no—
159#95×C47—21no—
160#95×C47—21no—
161#95×C47—21no—
162#95×C47D411yescharacteristic
163#95×C47D411yescharacteristic
164C24×C47—21no—
165C24×C47—21no—
166C24×C47—21no—
167C24×C47—24no—
168C24×C47—42no—
169C24×C47—42no—
170C24×C47—42no—
171C24×C47—42no—
172C24×C47—81no—
173C24×C47—81no—
174C24×C47C2×D411yescharacteristic
175#41×C47—28no—
176#41×C47—44no—
177#41×C47—44no—
178#41×C47—44no—
179C2×Q8×C47—21no—
180C2×Q8×C47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—21no—
184C2×Q8×C47—21no—
185C2×Q8×C47—21no—
186C2×Q8×C47—21no—
187C2×Q8×C47—21no—
188C2×Q8×C47—21no—
189C2×Q8×C47—21no—
190C2×Q8×C47C2×D412yes—
191C2×D4×C47—28no—
192C2×D4×C47—24no—
193C2×D4×C47—21no—
194C2×D4×C47—21no—
195C2×D4×C47—21no—
196C2×D4×C47—21no—
197C2×D4×C47—21no—
198C2×D4×C47—21no—
199C2×D4×C47—21no—
200C2×D4×C47—21no—
201C2×D4×C47—21no—
202C2×D4×C47—21no—
203C2×D4×C47—21no—
204C2×D4×C47—21no—
205C2×D4×C47—21no—
206C2×D4×C47—44no—
207C2×D4×C47—44no—
208C2×D4×C47—44no—
209C2×D4×C47—42no—
210C2×D4×C47—42no—
211C2×D4×C47—42no—
212C2×D4×C47—42no—
213C2×D4×C47—42no—
214C2×D4×C47C2×D412yes—
215C2×D4×C47C2×D412yes—
216C2×D4×C47C2×D412yes—
217C2×D4×C47C2×D412yes—
218C2×D4×C47C2×D412yes—
219C22×C4×C47—21no—
220C22×C4×C47—21no—
221C22×C4×C47—21no—
222C22×C4×C47—21no—
223C22×C4×C47—21no—
224C22×C4×C47—21no—
225C22×C4×C47—21no—
226C22×C4×C47—21no—
227C22×C4×C47—21no—
228C22×C4×C47—42no—
229C22×C4×C47—42no—
230C22×C4×C47—42no—
231C22×C4×C47—42no—
232C22×C4×C47—42no—
233C22×C4×C47—42no—
234C22×C4×C47—42no—
235C22×C4×C47—81no—
236C22×C4×C47—81no—
237C22×C4×C47C2×D411yescharacteristic
238C22×C4×C47C2×D411yescharacteristic
239C22×C4×C47C2×D411yescharacteristic
240C22×C4×C47C2×D411yescharacteristic
241C22×C4×C47C2×D412yes—
242C22×C4×C47C2×D411yescharacteristic
243C22×C4×C47#4112yes—
244C22×C4×C47C2411yescharacteristic
245SD16×C47—28no—
246SD16×C47—28no—
247SD16×C47—44no—
248SD16×C47—44no—
249D8×C47—28no—
250D8×C47—28no—
251M16×C47—28no—
252C2×C8×C47—21no—
253C2×C8×C47—21no—
254C2×C8×C47—21no—
255C2×C8×C47—21no—
256C2×C8×C47—21no—
257C2×C8×C47—21no—
258C2×C8×C47—21no—
259C2×C8×C47—21no—
260C2×C8×C47—21no—
261C2×C8×C47—21no—
262C2×C8×C47C2×D412yes—
263C2×C8×C47C2×D412yes—
264C4⋊C4×C47—21no—
265C4⋊C4×C47—21no—
266C4⋊C4×C47—21no—
267C4⋊C4×C47—21no—
268C4⋊C4×C47—21no—
269C4⋊C4×C47—21no—
270C4⋊C4×C47—42no—
271C4⋊C4×C47—42no—
272C4⋊C4×C47—42no—
273C22⋊C4×C47—22no—
274C22⋊C4×C47—41no—
275C22⋊C4×C47—42no—
276C22⋊C4×C47—42no—
277C22⋊C4×C47—42no—
278C22⋊C4×C47—42no—
279C22⋊C4×C47—42no—
280C22⋊C4×C47—42no—
281C22⋊C4×C47—42no—
282C22⋊C4×C47—42no—
283C22⋊C4×C47—42no—
284C22⋊C4×C47—42no—
285C22⋊C4×C47—81no—
286C22⋊C4×C47—81no—
287C42×C47—21no—
288C42×C47—21no—
289C42×C47—21no—
290C42×C47—21no—
291C23×C47—22no—
292C23×C47—22no—
293C23×C47—22no—
294C23×C47—21no—
295C23×C47—21no—
296C23×C47—21no—
297C23×C47—21no—
298C23×C47—21no—
299C23×C47—21no—
300C23×C47—22no—
301C23×C47—22no—
302C23×C47—48no—
303C23×C47—48no—
304C23×C47—41no—
305C23×C47—41no—
306C23×C47—41no—
307C23×C47—41no—
308C23×C47—41no—
309C23×C47—41no—
310C23×C47—41no—
311C23×C47—41no—
312C23×C47—41no—
313C23×C47—41no—
314C23×C47—41no—
315C23×C47—41no—
316C23×C47—41no—
317C23×C47—41no—
318C23×C47—41no—
319C23×C47—41no—
320C23×C47—84no—
321C23×C47—84no—
322C23×C47—84no—
323C23×C47—84no—
324C23×C47—84no—
325C23×C47#12112yes—
326C23×C47C22×D411yescharacteristic
327Q8×C47—22no—
328Q8×C47—22no—
329Q8×C47—41no—
330Q8×C47—41no—
331Q8×C47—41no—
332Q8×C47—41no—
333Q8×C47—41no—
334Q8×C47—41no—
335D4×C47—22no—
336D4×C47—22no—
337D4×C47—22no—
338D4×C47—22no—
339D4×C47—22no—
340D4×C47—22no—
341D4×C47—22no—
342D4×C47—48no—
343D4×C47—48no—
344D4×C47—41no—
345D4×C47—41no—
346D4×C47—41no—
347D4×C47—41no—
348D4×C47#12014yes—
349C2×C4×C47—21no—
350C2×C4×C47—21no—
351C2×C4×C47—21no—
352C2×C4×C47—21no—
353C2×C4×C47—22no—
354C2×C4×C47—22no—
355C2×C4×C47—22no—
356C2×C4×C47—22no—
357C2×C4×C47—21no—
358C2×C4×C47—21no—
359C2×C4×C47—21no—
360C2×C4×C47—22no—
361C2×C4×C47—21no—
362C2×C4×C47—21no—
363C2×C4×C47—21no—
364C2×C4×C47—21no—
365C2×C4×C47—21no—
366C2×C4×C47—21no—
367C2×C4×C47—48no—
368C2×C4×C47—41no—
369C2×C4×C47—41no—
370C2×C4×C47—41no—
371C2×C4×C47—41no—
372C2×C4×C47—41no—
373C2×C4×C47—41no—
374C2×C4×C47—41no—
375C2×C4×C47—41no—
376C2×C4×C47—41no—
377C2×C4×C47—41no—
378C2×C4×C47—41no—
379C2×C4×C47—41no—
380C2×C4×C47—41no—
381C2×C4×C47—41no—
382C2×C4×C47—84no—
383C2×C4×C47—84no—
384C2×C4×C47#12112yes—
385C2×C4×C47AGL(1,ℤ/8)12yescomplemented
386C2×C4×C47C22×D411yescharacteristic
387C2×C4×C47C22×D411yescharacteristic
388C2×C4×C47C22×D411yescharacteristic
389C2×C4×C47C2×#4111yescharacteristic
390C2×C4×C47H(5,𝔽2)11yescharacteristic
391C2×C4×C47H(5,𝔽2)11yescharacteristic
392C8×C47—22no—
393C8×C47—22no—
394C8×C47—41no—
395C8×C47—41no—
396#24367C4711yesmaximal, characteristic, direct product factor, Sylow
397C22×C47—22no—
398C22×C47—24no—
399C22×C47—22no—
400C22×C47—22no—
401C22×C47—42no—
402C22×C47—41no—
403C22×C47—41no—
404C22×C47—42no—
405C22×C47—42no—
406C22×C47—41no—
407C22×C47—41no—
408C22×C47—42no—
409C22×C47—42no—
410C22×C47—42no—
411C22×C47—42no—
412C22×C47—42no—
413C22×C47—42no—
414C22×C47—42no—
415C22×C47—42no—
416C22×C47—42no—
417C22×C47—816no—
418C22×C47—81no—
419C22×C47—81no—
420C22×C47—81no—
421C22×C47—81no—
422C22×C47—81no—
423C22×C47—81no—
424C22×C47—81no—
425C22×C47—81no—
426C22×C47C2×#12111yescharacteristic
427C22×C47D4211yescharacteristic
428C22×C47D4211yescharacteristic
429C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
430C22×C47#57511yescharacteristic
431C22×C47#57711yescharacteristic
432C22×C47#57711yescharacteristic
433C4×C47—22no—
434C4×C47—22no—
435C4×C47—42no—
436C4×C47—41no—
437C4×C47—41no—
438C4×C47—41no—
439C4×C47—81no—
440C4×C47—81no—
441C4×C47—81no—
442C4×C47—81no—
443C4×C47C2×#12011yescharacteristic
444C4×C47#53411yescharacteristic
445C4×C47#54611yescharacteristic
446C4×C47#54611yescharacteristic
447C22×AGL(1,ℤ/8)C2×C4711yescharacteristic
448C2×#463C2×C4711yescharacteristic, complemented
449C2×#461C2×C4711yescharacteristic, complemented
450C2×#450C2×C4711yescharacteristic, complemented
451#2432C2×C4711yescharacteristic, complemented
452D4×C22⋊C4C2×C4711yescharacteristic, complemented
453#2055C2×C4711yescharacteristic, complemented
454#2054C2×C4711yescharacteristic, complemented
455#2013C2×C4711yescharacteristic, complemented
456#2012C2×C4711yescharacteristic, complemented
457#1894C2×C4711yescharacteristic, complemented
458#1879C2×C4711yescharacteristic, complemented
459#1877C2×C4711yescharacteristic, complemented
460#1851C2×C4711yescharacteristic, complemented
461#1788C2×C4711yescharacteristic, complemented
462C2×C47—42no—
463C2×C47—44no—
464C2×C47—82no—
465C2×C47—82no—
466C2×C47#241011yescharacteristic
467C2×C47#303611yescharacteristic
468C2×C47#304211yescharacteristic
469C2×C47#326511yescharacteristic
470C2×C47#326711yescharacteristic
471C2×C47#327211yescharacteristic
472C2×C47#327511yescharacteristic
473C22×#41C22×C4711yescharacteristic
474C23×D4C22×C4711yescharacteristic
475C2×AGL(1,ℤ/8)—24no—
476C2×AGL(1,ℤ/8)—24no—
477C2×AGL(1,ℤ/8)—24no—
478C22×SD16C22×C4711yescharacteristic
479C22×SD16C22×C4711yescharacteristic
480C22×SD16C22×C4711yescharacteristic
481C22×SD16C22×C4711yescharacteristic
482C22×D8C22×C4711yescharacteristic
483C22×D8C22×C4711yescharacteristic
484C22×M16C22×C4711yescharacteristic
485C2×C4⋊Q8C22×C4711yescharacteristic, complemented
486C2×#124C22×C4711yescharacteristic, complemented
487C2×C22⋊Q8C22×C4711yescharacteristic
488C2×C4×D4C22×C4711yescharacteristic
489C2×C4×D4C22×C4711yescharacteristic
490C22×C22⋊C4—21no—
491#463—24no—
492#461—24no—
493#450—24no—
494C2×C4⋊C8C22×C4711yescharacteristic, complemented
495C2×C4⋊C8C22×C4711yescharacteristic, complemented
496C2×#103C22×C4711yescharacteristic, complemented
497C2×#103C22×C4711yescharacteristic, complemented
498C2×#103C22×C4711yescharacteristic, complemented
499C2×#103C22×C4711yescharacteristic, complemented
500C2×#102C22×C4711yescharacteristic
501C2×#102C22×C4711yescharacteristic
502C2×#102C22×C4711yescharacteristic, complemented
503C2×#102C22×C4711yescharacteristic, complemented
504C2×C22⋊C8C22×C4711yescharacteristic
505#394—21no—
506#394—21no—
507#391C22×C4711yescharacteristic, complemented
508#390C22×C4711yescharacteristic
509#390C22×C4711yescharacteristic
510#390C22×C4711yescharacteristic, complemented
511#386—21no—
512#386—21no—
513#385—21no—
514#385—21no—
515#380C22×C4711yescharacteristic
516#379—21no—
517C4×C22⋊C4C22×C4711yescharacteristic
518#340C22×C4711yescharacteristic, complemented
519#340C22×C4711yescharacteristic, complemented
520#336C22×C4711yescharacteristic, complemented
521#336C22×C4711yescharacteristic, complemented
522C47#2436711yescharacteristic, direct product factor, Sylow
523C25—21no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—22no—
528C2×#41—41no—
529C2×#41—41no—
530C22×Q8C23×C4711yescharacteristic
531C22×Q8C23×C4711yescharacteristic
532C22×D4—22no—
533C22×D4—22no—
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—22no—
537C22×D4—41no—
538C22×D4—41no—
539C22×D4D4×C4714yes—
540C22×D4C23×C4711yescharacteristic
541C22×D4C23×C4711yescharacteristic
542C22×D4C23×C4711yescharacteristic
543C23×C4—21no—
544C23×C4—21no—
545C23×C4—21no—
546C23×C4C23×C4711yescharacteristic
547AGL(1,ℤ/8)—232no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—22no—
554C2×SD16—22no—
555C2×SD16—22no—
556C2×SD16—22no—
557C2×SD16—41no—
558C2×SD16—41no—
559C2×SD16D4×C4714yes—
560C2×D8—22no—
561C2×D8—22no—
562C2×D8—22no—
563C2×D8—22no—
564C2×D8—22no—
565C2×D8D4×C4714yes—
566C2×M16—22no—
567C2×M16—22no—
568C2×M16—22no—
569C22×C8C23×C4711yescharacteristic
570C22×C8C23×C4711yescharacteristic
571C22×C8C23×C4711yescharacteristic
572C22×C8C23×C4711yescharacteristic
573C4⋊Q8—22no—
574C4⋊Q8—41no—
575#124—22no—
576#124—41no—
577C22⋊Q8—22no—
578C22⋊Q8—22no—
579C4×D4—22no—
580C4×D4—22no—
581C4×D4—41no—
582C4×D4—41no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4C23×C4711yescharacteristic
587C2×C4⋊C4C23×C4711yescharacteristic
588C2×C4⋊C4C23×C4711yescharacteristic
589C2×C22⋊C4—21no—
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—44no—
602C2×C22⋊C4D4×C4711yescharacteristic
603C2×C22⋊C4D4×C4711yescharacteristic
604C2×C42C23×C4711yescharacteristic
605C2×C42C23×C4711yescharacteristic
606C4⋊C8—22no—
607C4⋊C8—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616C22⋊C8—22no—
617#95—21no—
618#95—21no—
619#95—21no—
620#95D4×C4711yescharacteristic
621#95D4×C4711yescharacteristic
622C24—21no—
623C24—21no—
624C24—21no—
625C24—24no—
626C24—42no—
627C24—42no—
628C24—42no—
629C24—42no—
630C24—81no—
631C24—81no—
632C24C2×D4×C4711yescharacteristic
633#41—28no—
634#41—44no—
635#41—44no—
636#41—44no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—21no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8C2×D4×C4712yes—
649C2×D4—28no—
650C2×D4—24no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—44no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—42no—
672C2×D4C2×D4×C4712yes—
673C2×D4C2×D4×C4712yes—
674C2×D4C2×D4×C4712yes—
675C2×D4C2×D4×C4712yes—
676C2×D4C2×D4×C4712yes—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—81no—
694C22×C4—81no—
695C22×C4C2×D4×C4711yescharacteristic
696C22×C4C2×D4×C4711yescharacteristic
697C22×C4C2×D4×C4711yescharacteristic
698C22×C4C2×D4×C4711yescharacteristic
699C22×C4C2×D4×C4712yes—
700C22×C4C2×D4×C4711yescharacteristic
701C22×C4#41×C4712yes—
702C22×C4C24×C4711yescharacteristic
703SD16—28no—
704SD16—28no—
705SD16—44no—
706SD16—44no—
707D8—28no—
708D8—28no—
709M16—28no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8C2×D4×C4712yes—
721C2×C8C2×D4×C4712yes—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—42no—
729C4⋊C4—42no—
730C4⋊C4—42no—
731C22⋊C4—22no—
732C22⋊C4—41no—
733C22⋊C4—42no—
734C22⋊C4—42no—
735C22⋊C4—42no—
736C22⋊C4—42no—
737C22⋊C4—42no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—21no—
748C42—21no—
749C23—22no—
750C23—22no—
751C23—22no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—22no—
759C23—22no—
760C23—48no—
761C23—48no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—84no—
779C23—84no—
780C23—84no—
781C23—84no—
782C23—84no—
783C23#121×C4712yes—
784C23C22×D4×C4711yescharacteristic
785Q8—22no—
786Q8—22no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8—41no—
792Q8—41no—
793D4—22no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—22no—
798D4—22no—
799D4—22no—
800D4—48no—
801D4—48no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4#120×C4714yes—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—22no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—48no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—84no—
841C2×C4—84no—
842C2×C4#121×C4712yes—
843C2×C4AGL(1,ℤ/8)×C4712yescomplemented
844C2×C4C22×D4×C4711yescharacteristic
845C2×C4C22×D4×C4711yescharacteristic
846C2×C4C22×D4×C4711yescharacteristic
847C2×C4C2×#41×C4711yescharacteristic
848C2×C4H(5,𝔽2)×C4711yescharacteristic
849C2×C4H(5,𝔽2)×C4711yescharacteristic
850C8—22no—
851C8—22no—
852C8—41no—
853C8—41no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—24no—
858C22—42no—
859C22—42no—
860C22—42no—
861C22—41no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—41no—
866C22—41no—
867C22—42no—
868C22—42no—
869C22—42no—
870C22—42no—
871C22—42no—
872C22—42no—
873C22—42no—
874C22—816no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22—81no—
882C22—81no—
883C22C2×#121×C4711yescharacteristic
884C22D42×C4711yescharacteristic
885C22D42×C4711yescharacteristic
886C22C2×AGL(1,ℤ/8)×C4711yescharacteristic
887C22C47×#57511yescharacteristic
888C22C47×#57711yescharacteristic
889C22C47×#57711yescharacteristic
890C4—22no—
891C4—22no—
892C4—42no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—81no—
897C4—81no—
898C4—81no—
899C4—81no—
900C4C2×#120×C4711yescharacteristic
901C4C47×#53411yescharacteristic
902C4C47×#54611yescharacteristic
903C4C47×#54611yescharacteristic
904C2—42no—
905C2—44no—
906C2—82no—
907C2—82no—
908C2C47×#241011yescharacteristic
909C2C47×#303611yescharacteristic
910C2C47×#304211yescharacteristic
911C2C47×#326511yescharacteristic
912C2C47×#326711yescharacteristic
913C2C47×#327211yescharacteristic
914C2C47×#327511yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×AGL(1,ℤ/8)×C47C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. C2×C47×#463C2semidirect
3. C2×C47×#461C2semidirect
4. C2×C47×#450C2semidirect
5. C47×#2432C2semidirect
6. D4×C22⋊C4×C47C2semidirect
7. C47×#2055C2semidirect
8. C47×#2054C2semidirect
9. C47×#2013C2semidirect
10. C47×#2012C2semidirect
11. C47×#1894C2semidirect
12. C47×#1879C2semidirect
13. C47×#1877C2semidirect
14. C47×#1851C2semidirect
15. C47×#1788C2semidirect
28. C2×C4⋊Q8×C47C22semidirect
29. C2×#124×C47C22semidirect
37. C2×C4⋊C8×C47C22semidirect
38. C2×C4⋊C8×C47C22semidirect
39. C2×#103×C47C22semidirect
40. C2×#103×C47C22semidirect
41. C2×#103×C47C22semidirect
42. C2×#103×C47C22semidirect
45. C2×#102×C47C22semidirect
46. C2×#102×C47C22semidirect
50. C47×#391C22semidirect
53. C47×#390C22semidirect
61. C47×#340C22semidirect
62. C47×#340C22semidirect
63. C47×#336C22semidirect
64. C47×#336C22semidirect
385. C2×C4×C47AGL(1,ℤ/8)semidirect
396. #24367C47direct (N × H)
448. C2×#463C2×C47semidirect
449. C2×#461C2×C47semidirect
450. C2×#450C2×C47semidirect
451. #2432C2×C47semidirect
452. D4×C22⋊C4C2×C47semidirect
453. #2055C2×C47semidirect
454. #2054C2×C47semidirect
455. #2013C2×C47semidirect
456. #2012C2×C47semidirect
457. #1894C2×C47semidirect
458. #1879C2×C47semidirect
459. #1877C2×C47semidirect
460. #1851C2×C47semidirect
461. #1788C2×C47semidirect
485. C2×C4⋊Q8C22×C47semidirect
486. C2×#124C22×C47semidirect
494. C2×C4⋊C8C22×C47semidirect
495. C2×C4⋊C8C22×C47semidirect
496. C2×#103C22×C47semidirect
497. C2×#103C22×C47semidirect
498. C2×#103C22×C47semidirect
499. C2×#103C22×C47semidirect
502. C2×#102C22×C47semidirect
503. C2×#102C22×C47semidirect
507. #391C22×C47semidirect
510. #390C22×C47semidirect
518. #340C22×C47semidirect
519. #340C22×C47semidirect
520. #336C22×C47semidirect
521. #336C22×C47semidirect
522. C47#24367direct (N × H)
843. C2×C4AGL(1,ℤ/8)×C47semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×AGL(1,ℤ/8)×C472
C2×C47×#4632
C2×C47×#4612
C2×C47×#4502
C47×#24322
D4×C22⋊C4×C472
C47×#20552
C47×#20542
C47×#20132
C47×#20122
C47×#18942
C47×#18792
C47×#18772
C47×#18512
C47×#17882
#2436747